A Linear Matrix Inequality (LMI) where and and is given. is a vector in .
Then, the linear map from to , where is a space of symmetric matrices with prescribed block diagonal structure, is associated such that . The range of this map is .
My Question is, how to obtain ??
I guess, that is a matrix which columns are the matrices .
And is then the column space of ??
And when I want to find a matrix which is orthogonal to , is it then a matrix which is orthogonal to ??
As you might have noticed, I've no idea what to do.
So, please help me.